$h(n) = 3n$ $g(t) = 5t^{2}+7t+5(h(t))$ $ h(g(2)) = {?} $
Answer: First, let's solve for the value of the inner function, $g(2)$ . Then we'll know what to plug into the outer function. $g(2) = 5(2^{2})+(7)(2)+5(h(2))$ To solve for the value of $g$ , we need to solve for the value of $h(2)$ $h(2) = (3)(2)$ $h(2) = 6$ That means $g(2) = 5(2^{2})+(7)(2)+(5)(6)$ $g(2) = 64$ Now we know that $g(2) = 64$ . Let's solve for $h(g(2))$ , which is $h(64)$ $h(64) = (3)(64)$ $h(64) = 192$